CONVECTION AND CLIMATE (C MULLER, SECTION EDITOR)

Aquaplanet Simulations of Tropical Cyclones

Timothy M. Merlis1 & Isaac M. Held2

Published online: 8 June 2019# The Author(s) 2019

AbstractPurpose of Review Tropical cyclones (TCs) are strongly influenced by the large-scale environment of the tropics and will,therefore, be modified by climate changes. Numerical simulations designed to understand the sensitivities of TCs to environ-mental changes have typically followed one of two approaches: single-storm domain sizes with convection-permitting resolutionand uniform thermal boundary conditions or comprehensive global high-resolution (about 50 km in the horizontal) atmosphericgeneral circulation model (GCM) simulations. The approaches reviewed here rest between these two and are an importantcomponent of hierarchical modelling of the atmosphere: aquaplanet TC simulations.Recent Findings Idealized model configurations have revealed controls on equilibrium TC size in large-domain simulations ofrotating radiative-convective equilibrium. Simulations that include differential rotation (spherical geometry) but retain uniformthermal forcing have revealed a new mechanism of TC propagation change via storm-scale dynamics and show a poleward shiftin genesis in response to warming. Simulations with Earth-like meridional thermal forcing gradients have isolated competinginfluences on TC genesis via shifts in the atmospheric general circulation and the temperature dependence of TC genesis in theabsence of mean circulation changes.Summary Aquaplanet simulations of TCs with variants that include or inhibit certain processes have recently emerged as aresearch methodology that has advanced the understanding of the climatic controls on TC activity. Looking forward, idealizedboundary condition model configurations can be used as a bridge between GCM resolution and convection-permitting resolutionmodels and as a tool for identifying additional mechanisms through which climate changes influence TC activity.

Keywords Tropical cyclone . Aquaplanet . Climate model . Climate change

Introduction

Tropical cyclones (TCs, also known as hurricanes and ty-phoons) are a destructive component of the climate system.Given their importance, both observational analyses and nu-merical simulations of TCs are valuable research approaches[1•]. There is a longstanding desire to perform initialized, real-time forecasts to enable accurate prediction of TC track andintensity to minimize the loss of human life and property dam-

age from these powerful storms. Numerical simulation hasalso been used for many decades to do process studies, de-signed to elucidate the fundamental controls on TCs (e.g., [2]).

Anthropogenic climate change provides an important mo-tivation to identify how a warming tropical environment af-fects TCs. Given the well-documented environmental controlson TCs’ intensity, genesis, and tracks, climate model projec-tions of future climates inform expectations for future TCactivity. There is a consensus expectation about the projectionfor the maximum intensity, based on a combination of phys-ical modelling and theory. Other measures of TC activity,however, have larger uncertainty. An illustrative examplearises when trying to solely use observational estimates fromtoday’s climate together with information about climatechange obtained from coupled model simulations for TC gen-esis: different environmental genesis indices may be equallyconsistent with today’s climate yet project different changes infuture TC genesis. For example, Vecchi et al. (2008) [3] showthat different indices based on sea surface temperature (SST)

This article is part of the Topical Collection on Convection and Climate

* Timothy M. Merlistimothy.merlis@mcgill.ca

1 Atmospheric and Oceanic Sciences, McGill University, 805Sherbrooke Street West, Montreal, QC H3A 0B9, Canada

2 National Oceanic and Atmospheric Administration, GeophysicalFluid Dynamics Laboratory, Princeton, NJ, USA

Current Climate Change Reports (2019) 5:185–195https://doi.org/10.1007/s40641-019-00133-y

provide plausible reconstructions of historical TC activity, yetdivergent future projections. Likewise, multivariate genesisindices can have different weights of positive (humidity) andnegative (vertical wind shear) variables or somewhat differentvariables (such as measures of tropospheric humidity) thatlead to different projections for the future (e.g., [4–6]). Thissuggests a need to go beyond empirical approaches and high-lights the importance of physical models of the tropicalatmosphere.

General circulation model (GCM) simulations of TC activ-ity have improved since the mid-2000s (e.g., [7–11, 12•]).These simulations typically have reasonable geographic andseasonal distributions of TC genesis and therefore global TCnumber. They also simulate outer TC size that compares wellwith observations [13]. However, their intensity distributionsare sensitive to convective and other sub-grid scale parame-terization [14, 15] and are biased low at readily achievableresolutions (∼ 50 km), with improve distributions as horizon-tal resolution increases [e.g., 16]. This suggests that the pro-cesses controlling TC genesis and TC intensity are not inti-mately linked, and the genesis investigations in TC-permittingGCMs have led to the expectation of fewer TCs in a warmedfuture climate [10, 17], though the mechanism for this reduc-tion is not fully understood.

Contemporaneously, climate change–motivated single-TCsimulations furthered the understanding of environmentalcontrols on intensification (e.g., 18–20]). These simulationsoften use idealized boundary conditions (BCs) of doubly pe-riodic f -plane geometry with a homogeneous thermal forcing(prescribed uniform SST, in particular), run at sufficientlyhigh, Bcloud-resolving model^ (CRM) resolution (∼ 1km )to capture storm intensity (Fig. 1a). These studies illustratethe value of idealized BCs in understanding how TC intensi-fication changes with the mean thermodynamic environmentof the tropics. It is then natural to adopt a similar, idealized BCapproach in GCMs.

The canonical simplification to atmospheric GCMs, whichhas been used extensively to examine large-scale climatechanges, is to simplify the lower BC to that of a water-covered surface or Baquaplanet.^ This is typically done in amanner that eliminates zonal asymmetries (Fig. 1d). Given theclimate’s dominant variations are in latitude, this is a usefulframework to understand the response of the Hadley circula-tion, extratropical storm tracks, the meridional structure oftemperature, and the zonal-mean precipitation to climatechanges (e.g., [21–24]). The extent to which this is a usefulsimulation framework to understand climate influences onTCs is, perhaps, less obvious. Regionally specific aspects ofthe controls on TCs (e.g., the relationship to African easterlywaves) will be altered or eliminated by the use of aquaplanetBCs. However, there are successful applications of aquaplanetsimulations of TCs—similar to CRM simulations of a singleTC—that are valuable for a range of specific TC-climate

research questions. The aim of this review is to highlight suc-cessful uses of aquaplanet simulations for TC research andoutline future promising directions using this approach. Inparticular, comparisons of idealized BCs between CRM sim-ulations and GCM simulations is a promising avenue of eval-uating GCM parameterizations.

In what follows, we review the choices of simulation do-main and BCs that have been used for TC aquaplanet simula-tions (BSimulation Domain and Boundary Conditions^).Then, we review the recent scientific results that have beenobtained using this approach (BRecent Scientific Results^).Last, we discuss the outlook for this research approach andsuggest promising future directions (BOutlook^).

Simulation Domain and Boundary Conditions

Simulation Domain and Thermal Forcing

Earth’s rotation is critical to TCs, as is clear from the absenceof near-equator TCs (e.g., [25]). Therefore, the minimal sim-ulation domain is to have a non-zero, but constant Coriolisparameter: f -plane geometry (Fig. 1a and b). For small do-mains, a single TC is simulated and many studies consider theintensification in initial value problem simulations (e.g.,18–20, 26–28]), and these simulations are critical in develop-ing and evaluating theories for the dynamics of individual TCs[reviewed by 29]. There are also single-TC simulations oflonger time integrations [e.g., 30–32], which connects thesingle-TC research to the boundary value problem calcula-tions performed with large-domain rotating radiative-convective equilibrium (RCE). As the domain size is in-creased to those comparable to Earth’s surface area, multipleTCs are simultaneously simulated (Fig. 1b), and when run to astatistical steady state with uniform thermal forcing, this is arotating RCE. The BLarge-Domain, Rotating RadiativeConvective Equilibrium^ section reviews large-domain rotat-ing RCE simulation results.

Earth’s spherical geometry leads to two fundamental inho-mogeneities for climate. First, the projection of Earth’s spinaxis into the component normal to the surface—determiningthe Coriolis force acting on the horizontal wind—varies withlatitude (Fig. 2a). This gives rise to the β effect, i.e., the north–south variation of the Coriolis parameter f, which has funda-mental dynamical consequences for TC storm motion andtracks (Fig. 2b and c). A configuration that is a step towardcomprehensive simulations of Earth’s atmosphere from large-domain rotating RCE is then spherical geometry with uniformthermal forcing (Fig. 1c). The BSpherical Geometry WithUniform Thermal Forcing^ section reviews the results of sim-ulations in this configuration.

Earth’s spherical geometry also leads to the dependence ofthe solar zenith angle on latitude (Fig. 3a), giving rise to

186 Curr Clim Change Rep (2019) 5:185–195

equator-to-pole insolation (Δs) and temperature contrasts.Insolation gradients may take the form of perpetual equinoxconditions and include the diurnal cycle (e.g., [33]) or idealizedmeridional distributions that approximate the annual mean in-solation and are time-independent (e.g., [34]). Enabling thesethermodynamic and concomitant dynamic inhomogeneities(e.g., vertical wind shear in thermal wind balance with meridi-onal temperature gradients) that suppress extratropical TC ac-tivity [4, 35] leads to BEarth-like^ aquaplanets (Fig. 1d). TheBEarth-Like Aquaplanets^ section reviews TC-permitting sim-ulation results in this configuration.

This series of model configurations was outlined in thereview of Jeevanjee et al. [36•] as a possible Belegant tropicalmodel hierarchy.^ Hierarchical modelling of the atmosphere,with an emphasis on larger scales, has also been recentlyreviewed by [37]. Model hierarchies often prove to be usefulwhen they are used across a range of scientific questions [38],so while we review TC research here, there are a broader rangeof fundamental questions of tropical climate that the sameconfigurations can be used to address (BOutlook^).

We focus on results performed across this hierarchy ofsimulation configurations performed with the GeophysicalFluid Dynamics Laboratory’s High-Resolution AtmosphericModel (HiRAM) GCM, which has a high-quality simulationof climatological, interannual, and interdecadal TC activity incomprehensive BC simulations with prescribed, interannually

varying, observed SST [9, public release available at https://www.gfdl.noaa.gov/hiram-quickstart/]. The observationalevaluation of comprehensive BC simulations is a criticalstep in working with a model hierarchy and is one thatshould be undertaken with global CRMs as they emerge.HiRAM is a GCM with which simulations in allconfigurations described have been performed. Wherepossible, we compare with CRM or other high-resolutionGCM results in these configurations.

Lower Boundary Condition

An aquaplanet BC is a water-covered, saturated surface. Thelower surface BC can either have a prescribed SST [33] or aslab ocean BC (e.g., [43, 44]). Prescribed SST BCs have thevirtue that they can be used to isolate differences in the atmo-spheric simulations and are therefore routinely used in modelintercomparisons, including aquaplanet fifth phase of thecoupled model intercomparison project CMIP5 simulation de-sign [45, 46] and the high-resolution GCM intercomparisondescribed in Walsh et al. [47]. This has been used as a lowerBC in Earth-like aquaplanet TC-permitting GCM simulationsby Li et al. [48] and Ballinger et al. [34].

Slab ocean BCs allow the SST to respond to turbulentsurface fluxes and radiative fluxes, thereby closing the surfaceenergy budget without unphysical implied fluxes. This has

Fig. 1 Domains and thermalforcing for idealized tropicalcyclone model configurations.Uniform thermal forcing, doublyperiodic, constant Coriolisparameter (f -plane) rotatingconfigurations for a small and blarge domains, which formrotating radiative-convectiveequilibria for long timeintegrations. Spherical geometrydomains, where β = ∂yf≠ 0 with cuniform and d Earth-like thermalforcing (meridional insolationgradient Δs≠ 0) with shadingindicating surface temperature(yellow indicating warmertemperature than blue). Note theTC size is exaggerated comparedto the domain size in theseschematics

Curr Clim Change Rep (2019) 5:185–195 187

been used in aquaplanet GCM simulations of TCs by Merliset al. [40], Viale and Merlis [41], and Zhou et al. [49]. Theturbulent latent heat fluxes are critical to TC intensificationand can reach large values (order 1000Wm− 2) near the TCcenter [50]. This is a cooling tendency on the surface thatprescribed SSTsimulations neglect [a sensitivity systematical-ly examined in slab ocean simulations of large-domain rotat-ing RCE in 49]. However, the slab ocean BC is assumed tohave an infinite diffusivity and therefore vertically uniformtemperature, which precludes the mixing effects of TC stirringcold water up from the subsurface ocean [e.g., 51, 52].

Recent Scientific Results

Large-Domain, Rotating Radiative ConvectiveEquilibrium

There have been many initial value problem calculations withsmall domains (≈ 1000km; Fig. 1a) with convection-permittingresolution (CRMs). These typically have prescribed SST andare integrated for ≈ 10 days, as is relevant for TC intensificationfrom an initial vortex (e.g., [19]). The climate complement ofthis calculation is a boundary value problem, integrated to a

statistically steady state (≈ 100 days) with a domain that issufficiently large (≈ 10,000 km; Fig. 1b) to enable the simula-tion of multiple TCs [pioneered by 53]. Large-domain rotatingRCE simulations have been performed with both GCM (e.g.,[53, 54]) and CRM [55] resolution, though Khairoutdinov andEmanuel [55] increased the Coriolis parameter by about anorder of magnitude to allow multiple TCs in a smaller domain.A variant of large-domain rotating RCE has been performedwith spherical-domain GCMswith the Coriolis parameter is setto a uniform value at all latitudes [56, a configuration with aninconsistency in angular momentum conservation, Fig. 2a].This may be an easier configuration to set up in spherical ge-ometry GCM dynamical cores than rotating RCE withCartesian f -plane geometry and plausibly does not distort TCdynamics. Note, however, that this is a distinct configurationfrom the spherical geometry with uniform thermal forcing con-figuration described in BSpherical Geometry With UniformThermal Forcing.^

In large-domain, rotating RCE simulations, TCs developand fill the domain. The statistical equilibrium is one of infre-quent genesis and lysis. The dry, subsiding region away fromthe TCs is a thermodynamic barrier that may inhibit TC–TCinteractions like mergers. The scientific questions that havebeen addressed include the equilibrium TC size and intensity,

Fig. 2 Spherical geometry withuniform thermal forcing simulatesthe effects on tropical cyclones ofthe inhomogeneous Coriolisparameter. a Coriolis parameter’slatitudinal variation, the β-effect.b The β-drift mechanism forwestward and poleward TCpropagation, where H and L areregions of high and low relativevorticity induced by theconservation of absolute vorticity.c The average track of a sphericalgeometry GCM simulation withuniform thermal forcing followsβ-drift’s poleward and westwardtrajectory (reprinted from [39]). d,e Polar projection ofinstantaneous surface windspeedfor two SSTs (reprinted from[40∙]) with 30∘ latitude circlesindicated with dotted lines

188 Curr Clim Change Rep (2019) 5:185–195

with a focus on SSTand Coriolis parameter (i.e., rotation rate)sensitivity. TC size and intensity increase with temperature.As f increases, the TC size decreases and the intensity in-creases. The TC size roughly scale with both the deformationradiusNHf− 1, where N is the buoyancy frequency andH is thetroposphere depth, and the length scale given by the ratio ofTC potential intensity (PI) VPI to f (Held and Zhao [53],though Zhou et al. [54] have distinguished inner and outerTC sizes). These sensitivities are qualitatively consistent withtwo dimensional, single-TC simulations [31]; however,Chavas and Emanuel [31] distinguished between the PI lengthscale and deformation radius in simulations with altered radi-ative cooling, and the PI scale was found to be consistent withthe numerical simulation results.

The extent to which large-domain rotating RCE’s sensitivi-ties are relevant for Earth’s climate, such as anthropogenicwarming, is unclear because the equilibrium takes a fairly longtime to establish and the environment is strongly modified by

the TCs themselves (e.g., the tropospheric humidity distributiondiffers from small-domain RCE or comprehensive GCM sim-ulations of Earth). These differences motivate a careful analysisof spherical domain simulations, where TCs can propagate,leaving the genesis environment to be restored by non-TC con-vective, radiative, and dynamical tendencies (Fig. 1c).

Spherical Geometry With Uniform Thermal Forcing

Spherical (or β-plane) geometry introduces dynamical effectsarising from the non-uniform Coriolis parameter. The nonlin-ear self-advection of tropical cyclones or Bβ drift^ accountsfor the poleward and westward TC propagation that is a ubiq-uitous feature of TC tracks [57]. The relative vorticity pertur-bations induced by absolute vorticity conservation (equiva-lently, barotropic potential vorticity conservation) of the pole-ward vs. equatorward flowing air gives rise to secondary cir-culation tendencies that induce a poleward and westward TC

Fig. 3 Earth-like thermal forcing generates mean circulations that affectTCs and their response to climate changes. a Insolation’s latitudinalvariation. b Schematic of the zonal-mean overturning circulation(Hadley) with TC genesis on the poleward edge of the ITCZ. cInstantaneous surface wind speed (colors) and precipitation rate (bluecontour of 15mmday− 1, reprinted from [41]). d Global number of TCsin slab ocean simulations of radiatively forced climate changes with un-changed ocean heat transport vs ITCZ latitude with solar constant S0 in

Wm− 2 (reprinted from [42]). e Aquaplanet GCM simulation TC tracksand zonal-mean precipitation and genesis frequency (reprinted from[42]). f Global number of TCs in slab ocean simulations with radiativelyforced climate changes and perturbed ocean heat transport vs. ITCZ lat-itude, with Q0 value indicated the magnitude of prescribed ocean heattransport convergence with downward arrows indicating the estimate thatwarmed climates have 10% K− 1 fewer TCs than corresponding controlclimates with similar ITCZ position (reprinted from [42])

Curr Clim Change Rep (2019) 5:185–195 189

motion (Fig. 2b). Therefore, spherical or β-plane geometrywith uniform thermal forcing is the minimal simulation con-figuration that allows for TC propagation away from the gen-esis region, while retaining the homogeneous BCs for thermo-dynamic variables. The first published study that analyzedTCs in this configuration was Shi and Bretherton [39], whoshowed the typical TC track underwent β drift all the way tothe pole (Fig. 2c)! The resulting turbulent equilibrium is onewhere TCs densely populate a polar cap (Fig. 2d, e), and thereare frequent TC–TC interactions (including the BFujiwharaeffect^ of co-rotation, animation available here https://vimeo.com/159153890) with merger events that are morecommon than in large-domain rotating RCE.

This simulation configuration had previously been used toexamine Hadley circulations in the regime where the axisym-metric theories [58] do not support overturning circulationsbecause of the absence of meridional thermal gradients[59–61]. Note that we avoid using the term Bglobal RCE^for this configuration, as the simulated time-mean divergentcirculations (e.g., Fig. 2 of [62]) affect the troposphere’s ener-gy balance, though other authors have used this term to de-scribe this model configuration. Subsequent to Shi andBretherton [39], Merlis et al. [40•] showed the temperaturesensitivity of the number, intensity, and genesis rate in thisconfiguration. These were compared to the large-domain ro-tating RCE f -plane simulations of Zhou et al. [54], and manyof the sensitivities qualitatively carry over. For example,Merlis et al. [40•] found that there were fewer TCs withwarming, a sensitivity also found in another GCM [63], andthat the genesis rate decreased with warming. Chavas andReed [64•] systematically varied rotation rate and planet radi-us to more thoroughly assess the extent to which f -planesensitivities carry over to spherical geometry. The TCpressure-wind relationship in this configuration has also beencompared with a comprehensively configured GCM and ob-servations, and there is consistency with a theoretical relation-ship based on gradient wind balance that holds across themodel hierarchy and in observations [65•]. A new scientificresult was that the TC propagation speed, via β drift, increasedwith warming [40•]. The increased β drift with warming arisesfrom both larger storm radius and intensity (Fig. 2d and e).This increased β drift with warming has also been found insingle-TC, convection-permitting simulations [Chapter 3 of66]. The observed slowdown in TC propagation [67] is affect-ed by steering wind changes of the larger-scale atmosphericcirculation, and this discrepancy is suggestive that β driftchanges revealed by this model configuration are subdomi-nant to other mechanisms.

These simulations have a well-defined, low-latitude (near15∘) TC genesis region that moves poleward with warming,leaving an enlarged TC-free equatorial zone (Fig. 2d,e).Interestingly, this is consistent with downscaled TC simula-tions of substantially warmed, comprehensive BC GCM

simulations (Fig. 3 of [68]). It is also potentially relevant toobserved poleward shifts in TC statistics (e.g., [69]), thoughthe simulated poleward shift per unit of tropical warming isabout an order of magnitude smaller than observed. This typeof discrepancy implies either changes beyond those capturedby this model configuration are important or internal variabil-ity is a substantial component of observed changes. One in-terpretation of the poleward shift in genesis in simulationswith uniform thermal forcing is to consider it an expansionof the Bforbidden^ near-equatorial zone where the require-ment that the TC size is small enough to fit within a singlehemisphere is not met [64•]. As equilibrium TC size dependson thermodynamic quantities, like potential intensity VPI orthe dry static stability (∝ N) that increase with warming, theminimum required distance from the equator increases as thisstorm size increases. However, the controls on TC size atgenesis likely differ from the better-understood equilibriumsize and spherical geometry has other factors that influencegenesis (weak time-mean divergent circulations andconvectively coupled waves).

Earth-Like Aquaplanets

Moving from uniform thermal forcing to Earth-likeaquaplanets, an extratropical baroclinic region with verticalwind shear emerges (Fig. 1c–d) and strong time-mean diver-gent circulations shape the tropical regions favorable for TCgenesis (Fig. 3b, c, e). One could systematically vary the me-ridional SST gradient to connect these regimes, a parametervariation that Fedorov et al. [70•] examined. They found thatextratropical regions of warm-core cyclone (TC) activity (near≈ 40∘) was eliminated when the equator-to-pole SST contrastwas increased from a small value of 14K to a value morecharacteristic of Earth’s late summer of 23K.

For interactive SST BCs, aquaplanets with Earth-like ther-mal forcing have been performed with perpetual equinox, per-petual annual mean, or seasonally varying insolation. As iswell known observationally, the seasonal cycle is importantfor TCs. The seasonal cycles of the general circulation andsurface climate in aquaplanets with slab ocean BCs dependon the surface heat capacity, and these sensitivities are thesubject of investigation in and of themselves (e.g., [71–73]).Therefore, time-independent, hemispherically asymmetricforcing (akin to perpetual late-summer conditions) has beenused for Earth-like aquaplanets in TC research. This is alsocomputationally advantageous, as a shorter spin-up time isrequired to reach an equilibrated climate state (≈ 5 years ratherthan ≈ 10 years).

As the degree of hemispheric asymmetry is varied in Earth-like aquaplanets, there are large sensitivities in TC activity. Inthe hemispherically symmetric case, there may be little TCactivity because the intertropical convergence zone (ITCZ)and concomitant high free-tropospheric humidity are on the

190 Curr Clim Change Rep (2019) 5:185–195

equator, where the Coriolis parameter is zero. Figure 3(bottom) shows the increase in TC genesis as the ITCZ isdisplaced from the equator [42]. These simulations havetime-independent hemispherically symmetric insolation anda hemispherically asymmetric prescribed cross-equatorialocean heat transport convergence, following Kang et al.[44]. As the cross-equatorial ocean heat transport is increased(shown in gray symbols), the ITCZ shifts further off equatorand the number of TCs increases strongly: In this GCM, it is a≈ 40% increase per degree latitude ITCZ shift (measured bythe latitude of maximum precipitation [42]). We note that thesimulations with more poleward ITCZ latitudes also havewider convergence zones (see review by [74]), a factor thatmay also be conducive to TC genesis as the meridional scaleof the high humidity region is larger.

The Earth-like aquaplanet simulations shown in Fig. 3dhave a distinctive response to radiatively forced warming.For an unchanged value of cross-equatorial ocean heat trans-port, there is an increase in TC genesis. This stands in contrastto comprehensively configured version of this GCM. The in-crease in aquaplanet TCs arises as a result of the competingeffects of warming, which tends to reduce genesis with un-changed ITCZ location, and a poleward ITCZ shift, which canoccur with constant cross-equatorial ocean heat transport be-cause of atmospheric radiative feedbacks and stratificationchanges [75•], that tends to increase genesis. This is capturedby the following partial sensitivities for the global TC numberN:

N−1∂N=∂ϕI≈40% ∘latð Þ−1 ð1ÞN−1∂N=∂T≈−10%K−1; ð2Þwith ITCZ latitude ϕI and tropical-mean surface temperatureT. For this GCM, the ITCZ shifts in response to warming byabout + 0.6∘latK− 1, implying the ITCZ-related increase islarger than the decrease in TCs fromwarming with unchangedITCZ position. Figure 3f shows this simple estimate of howthe number of TCs in the simulations with Earth-like CO2 andsolar constant would be expected to change if the warmingsensitivity was taken into account (downward pointing arrowsin Fig. 3f). For example, the 4 × CO2 simulation has an ITCZnear 11∘ (purple square in Fig. 3f) and is ≈ 3K warmer in thetropics than the 1 × CO2 with similar ITCZ latitude (seconddarkest gray circle in Fig. 3f), implying a ≈ 30% reduction ofTCs would be expected from warming (2). The reduction inexplicitly simulated TCs in the 4 × CO2 simulation (purplesquare in Fig. 3f) is indeed approximately consistent with theestimated reduction (purple circle in Fig. 3f). It is an intriguingpossibility that the mechanism underlying the reduction ingenesis with unchanged ITCZ position in the Earth-likeaquaplanets is the same as that of the aquaplanet with uniformthermal forcing; this has not been investigated and is a prom-ising direction toward building confidence in the robustness of

comprehensive GCM results, which typically have genesisreductions in warming scenarios.

The poleward ITCZ shift in response to CO2 is a robustresponse in Earth-like aquaplanet simulations, according to aGCM intercomparison [75•]. We note that the seasonal sensi-tivity of the ITCZ may respond differently than these Earth-like aquaplanets with time-independent BCs. Systematic in-vestigation of the TC genesis response to ITCZ latitude havenot been examined in other TC-permitting GCMs, an impor-tant sensitivity to assess in other models.

The sensitivities appear broadly similar between CO2 andsolar radiative forcing in Fig. 3b. A closer examination revealsthat there is a larger increase in response to CO2-forcedwarming than that of solar forcing [41]. This is related to aradiative forcing agent dependence of the ITCZ shift: there is alarger shift provoked by CO2, per unit warming or unit radia-tive forcing, that arises from differences in the spatial structureof the radiative forcing [41]. Solar forcing is larger magnitudein low latitudes than CO2 forcing, which implies a more mod-est ITCZ shift, according to energetic theories for ITCZ shifts[76]. This is dynamical mechanism for radiative forcing agentdependence of TC responses is distinct from proposed ther-modynamic mechanisms associated with changes in potentialintensity changes [77, 78]. That thermodynamic mechanismof radiative forcing agent dependence is related to variationsbetween solar and greenhouse forcing in altering tropical-mean energy budgets [79, 80].

Here we have reviewed the genesis results in Earth-likeaquaplanets, but other aspects such as TC track, lifetime, av-erage intensity (see [34]), influences of changes in the midlat-itude atmospheric circulation, and extratropical transition arefruitful avenues of future inquiry.

Outlook

The last decade of research has seen significant progress inusing idealized boundary condition (BC) configurations ofatmospheric models to simulate and understand tropical cy-clones (TCs). A hierarchy of domains and thermal forcinghave filled a gap between the small-domain f -plane simula-tions with uniform thermal forcing of a single-TC and theglobal TC-permitting resolution GCM simulations with com-prehensive Earth BCs (Fig. 1). This hierarchy includes large-domain rotating radiative-convective equilibria, where a tur-bulent equilibrium emerges with multiple TCs (Fig. 1b).Dynamical effects of spherical geometry can then be intro-duced in spherical (or β-plane) geometry simulations withuniform thermal forcing, where a well-defined subtropicalTC genesis rate can be quantified because the β-drift propa-gation mechanism is a TC removal mechanism from theselatitudes (Figs. 1c and 2b). Then, inhomogeneous thermalforcing can be introduced in spherical domain simulations

Curr Clim Change Rep (2019) 5:185–195 191

with zonally symmetric, but Earth-like thermal forcing andBCs (BEarth-like^ aquaplanets). This creates extratropical re-gions with meridional temperature gradients and the concom-itant vertical wind shear, which are unfavorable for TCs, anddivergent circulations that shape favorable low-latitude re-gions for TC genesis (Figs. 1d and 3b).

The results to date have shown environmental temperatureand rotation rate sensitivities, and large-scale circulation ef-fects that are valuable for understanding TC sensitivities andmay help decompose the results of global GCM simulationswith comprehensive Earth BCs. Proceeding through the hier-archy is also illustrative in highlighting sensitivities whenthere are differences between configurations. For example,large-domain rotating RCE, spherical geometry with uniformthermal forcing, and comprehensive Earth BC simulations inHiRAM have reduced numbers of TCs with warming whenperturbed by uniform SST increases, yet the Earth-likeaquaplanet has an increase in the number of TCs when a slabocean BC with an energetically consistent pattern of warmingemerges in response to increased CO2.

In the analysis of the HiRAM GCM, the sensitivity ofgenesis frequency changes in the uniform thermal forcing isbroadly [40•] similar to the Earth-like aquaplanet response towarming [42], which in turn, is broadly similar to comprehen-sive BC perturbation simulations [9, 11]. This is suggestive ofthe same underlying mechanism for the genesis changes, butquantitative assessments of them (following, e.g., [81]) havenot been made across the hierarchy.

The Earth-like aquaplanet configuration naturally empha-sizes the role of north-south (Hadley) circulation changes onTCs. However, zonal asymmetries are important in determin-ing the climatological TC activity [including low-frequencyvariations 82, 83] and the zonal asymmetric component ofchanges are important in comprehensive GCM simulationsof TC changes (e.g., Fig. 16 of [9]). An appealing directionfor further research is to introduce zonal asymmetries, eitherwith land surfaces [84•] or with oceanic lower BCs (see pre-liminary explorations in [85, 86]).

Simulations across this range of model configurations havebeen performedwith GCMs that parameterize convection and,in certain configurations, with large-domain convection-per-mitting resolution. These comparisons across model type aresuggestive of the utility of using idealized TC-permitting con-figurations for model development. Concrete examples of thisinclude variable-resolution or stretched-grid dynamical cores[87, 88] and approaches to make CRMs more computationalaffordable [89]. The intercomparison of non-rotating RCE[90•] may be extended to some of the idealized configurationsdescribed here, such as uniform thermal forcing in spherical orβ-plane geometry. Last, it is worth noting that Earth-likeaquaplanet intercomparisons, such as that of CMIP5, typicallyuse hemispherically symmetric SST distributions that are un-favorable for TC genesis. It is, therefore, advisable to

systematically include hemispherically asymmetric SST dis-tributions in future aquaplanet intercomparisons.

Looking forward, there are a number of scientific questionsthat are ripe for assessment in the idealized model configura-tions described here. A central question of the tropical climateinvolves the mechanisms and extent to which convection andclouds aggregate [91, 92]. Temperature sensitivity of non-rotating convective aggregation has been found in CRM andGCM simulations [93, 94], which may have implications forclimate feedback processes. The introduction of rotation givesrise to TCs and the intraseasonal Madden-Julian Oscillation(MJO), and these may have distinct temperature sensitivity thatmodify the extent to which the non-rotating aggregation resultscarry over to the rotating sphere. Within the context of differ-entially rotating geometry with uniform thermal forcing, a basicquestion concerns the relative amplitudes and interactions be-tween convection organized into Rossby waves, Kelvin waves,MJO [62, 95], or TCs [39, 40•]. Across these phenomena (con-vection to TCs to MJO), a common framework of analysis is toconsider moist static energy variance budgets [27, 81, 93, 95,96]. Applying these diagnostics to aquaplanet simulations ofTCs is an important avenue to understanding how the processesleading to organization in non-rotating or single-TC f -planesimulations are affected as more Earth-like geometry and ther-mal forcing are successively introduced.

Acknowledgements T. M. acknowledges the support of Natural Scienceand Engineering Research Council of Canada grant RGPIN-2014-05416and a Canada Research Chair. We are grateful for thoughtful reviews byDan Chavas and an anonymous review, comments from Nadir Jeevanjee,and editorial help from Alex Phucas.

Compliance with Ethical Standards

Conflict of Interest On behalf of all authors, the corresponding authorstates that there is no conflict of interest.

Open Access This article is distributed under the terms of the CreativeCommons At t r ibut ion 4 .0 In te rna t ional License (h t tp : / /creativecommons.org/licenses/by/4.0/), which permits unrestricted use,distribution, and reproduction in any medium, provided you give appro-priate credit to the original author(s) and the source, provide a link to theCreative Commons license, and indicate if changes were made.

References

Papers of particular interest, published recently, have beenhighlighted as:• Of importance

1.• Emanuel K. 100 years of progress in tropical cyclone research.Meteorol Monogr 2019;59:15.1–15.68. This monograph coversa wide range of TC research from a historical perspective.

192 Curr Clim Change Rep (2019) 5:185–195

2. Rotunno R, Emanuel KA. An air–sea interaction theory for tropicalcyclones. Part II: Evolutionary study using a nonhydrostatic axi-symmetric numerical model. J Atmos Sci 1987;44:542–561.

3. Vecchi GA, Swanson KL, Soden BJ. Whither hurricane activity?Science 2008;322:687–689.

4. Emanuel KA, Nolan DS. Tropical cyclone activity and the globalclimate system. Preprints, 26th Conf. on Hurricanes and TropicalMeteorology, Miami, FL, Amer. Meteor. Soc. A, vol 10; 2004.

5. Tippett MK, Camargo SJ, Sobel A. A Poisson regression index fortropical cyclone genesis and the role of large-scale vorticity in gen-esis. J Climate 2011;24:2335–2357.

6. Tang B, Camargo SJ. Environmental control of tropical cyclones inCMIP5: Aventilation perspective. J Adv Model Earth Syst 2014;6:115–128.

7. Sugi M, Noda A, Sato N. Influence of the global warming ontropical cyclone climatology: An experiment with the JMA globalmodel. J Meteorol Soc Japan 2002;80:249–272.

8. Bengtsson L, Hodges KI, EschM, Keenlyside N, Kornblueh L, LouJJ, Yamagata T. How may tropical cyclones change in a warmerclimate? Tellus 2007;59A:539–561.

9. Zhao M, Held IM, Lin SJ, Vecchi GA. Simulations of global hur-ricane climatology, interannual variability, and response to globalwarming using a 50-km resolution GCM. J Climate 2009;22:6653–6678.

10. Zhao M, et al. Robust direct effect of increasing atmospheric CO2

concentration on global tropical cyclone frequency: A multimodelinter-comparison. US CLIVARVariations 2013;11:17–24.

11. Wehner M, Reed KA, Stone D, Collins WD, Bacmeister J.Resolution dependence of future tropical cyclone projections ofCAM5. 1 in the US CLIVAR Hurricane Working Group idealizedconfigurations. J Climate 2015;28:3905–3925.

12.• Camargo SJ,Wing AA. Tropical cyclones in climate models. WileyInterdiscip Rev Clim Chang 2016;7:211–237. This review articledescribes GCM simulations of TCs, as well as other techniquesthat have been used to assess changes in TC activity.

13. Schenkel BA, Lin N, Chavas D, Vecchi GA, Oppenheimer M,Brammer A. Lifetime evolution of outer tropical cyclone size andstructure as diagnosed from reanalysis and climate model data. JClimate 2018;31: 7985–8004.

14. Zhao M, Held IM, Lin SJ. Some counterintuitive dependencies oftropical cyclone frequency on parameters in a GCM. J Atmos Sci2012;69:2272–2283.

15. Shaevitz DA. Coauthors: Characteristics of tropical cyclones inhigh-resolution models in the present climate. J Adv Model EarthSyst 2014;6:1154–1172.

16. Murakami H. Coauthors: Simulation and prediction of category 4and 5 hurricanes in the high-resolution GFDL HiFLOR coupledclimate model. J Climate 2015;28:9058–9079.

17. Knutson TR, McBride JL, Chan J, Emanuel K, Holland G, LandseaC, Held I, Kossin J, Srivastava AK, Sugi M. Tropical cyclones andclimate change. Nat Geosci 2010;3:157–163.

18. Knutson TR, Tuleya RE. Impact of CO2-induced warming on sim-ulated hurricane intensity and precipitation: Sensitivity to the choiceof climate model and convective parameterization. J Climate2004;17:3477–3495.

19. Nolan DS, Rappin ED, Emanuel KA. Tropical cyclogenesis sensi-tivity to environmental parameters in radiative-convective equilib-rium. Quart J Roy Meteor Soc 2007;133:2085–2107.

20. Nolan DS, Rappin ED. Increased sensitivity of tropical cyclogene-sis to wind shear in higher SST environments. Geophys Res Lett2008;35(14):L14805.

21. Schneider T, O’Gorman PA, Levine XJ. Water vapor and the dy-namics of climate changes. Rev Geophys 2010;48:RG3001. https://doi.org/10.1029/2009RG000302.

22. Voigt A, Shaw TA. Circulation response to warming shaped byradiative changes of clouds and water vapour. Nat Geosci 2015;8:102–106.

23. Kang SM, Frierson DMW, Held IM. The tropical response toextratropical thermal forcing in an idealized GCM: the importanceof radiative feedbacks and convective parameterization. J AtmosSci 2009;66:2812–2827.

24. Henry M, Merlis TM. The role of the nonlinearity of the Stefan-Boltzmann law on the structure of radiatively forced temperaturechange. J Climate 2019;20:335–348.

25. Emanuel K. Tropical cyclones. Annu Rev Earth Planet Sci 2003;31:75–104.

26. Davis CA. The formation of moist vortices and tropical cyclones inidealized simulations. J Atmos Sci 2015; 72:3499–3516.

27. Wing AA, Camargo SJ, Sobel A. Role of radiative–convectivefeedbacks in spontaneous tropical cyclogenesis in idealized numer-ical simulations. J Atmos Sci 2016;73:2633–2642.

28. Murthy VS, Boos WR. Role of surface enthalpy fluxes in idealizedsimulations of tropical depression spinup. J Atmos Sci 2018;75:1811–1831.

29. Montgomery MT, Smith RK. Recent developments in the fluiddynamics of tropical cyclones. Ann Rev Fluid Mech 2017;49:541–574.

30. Hakim GJ. The mean state of axisymmetric hurricanes in statisticalequilibrium. J Atmos Sci 2011;68:1364–1376.

31. Chavas DR, Emanuel K. Equilibrium tropical cyclone size in anidealized state of axisymmetric radiative–convective equilibrium. JAtmos Sci 2014;71:1663–1680.

32. Persing J, Montgomery MT, Smith RK, McWilliam JC. Quasisteady-state hurricanes revisited. Trop Cyclone Res Rev 2019;8:1–17.

33. Neale RB, Hoskins BJ. A standard test for AGCMs including theirphysical parametrizations: I: The proposal. Atmos Sci Lett 2000;1:101–107.

34. Ballinger AP, Merlis TM, Zhao M, Held IM. The sensitivity oftropical cyclone activity to off-equatorial thermal forcing. J AtmosSci 2015;72:2286–2302.

35. Gray WM. Hurricanes: Their formation, structure and likely role inthe tropical circulation. Meteorology over the tropical oceans, pp.155–218. Royal Meteorological Society. In: Shaw DB, editors;1979.

36.• Jeevanjee N, Hassanzadeh P, Hill S, Sheshadri A. 2017. A perspec-tive on climate model hierarchies. J. Adv. Model. Earth Syst. pp.1760–1771. This article describes novel categorizations of cli-mate model hierarchies, which include broader range of modelconfigurations than those discussed here.

37. Maher P, Gerber EP, Medeiros B, Merlis TM, Sherwood S,Sheshadri A, Sobel A, Vallis GK, Voigt A, Zurita-Gotor P. 2019.Model hierarchies for understanding atmospheric circulation. Rev.Geophys. p. in press.

38. Held IM. The gap between simulation and understanding in climatemodeling. Bull Amer Meteor Soc 2005;86: 1609–1614.

39. Shi X, Bretherton CS. Large-scale character of an atmosphere inrotating radiative-convective equilibrium. J Adv Earth Model Syst2014;6:616–629.

40.• Merlis TM, Zhou W, Held IM, Zhao M. Surface temperature de-pendence of tropical cyclone-permitting simulations in a sphericalmodel with uniform thermal forcing. Geophys Res Lett 2016;43:2859–2865. This article compares simulations of spherical ge-ometry with uniform thermal forcing to large-domain rotatingRCE.

41. Viale F, Merlis TM. Variations in tropical cyclone frequency re-sponse to solar and CO2 forcing in aquaplanet simulations. J AdvModel Earth Syst 2017;9:4–18.

Curr Clim Change Rep (2019) 5:185–195 193

42. Merlis TM, ZhaoM, Held IM. The sensitivity of hurricane frequen-cy to ITCZ changes and radiatively forced warming in aquaplanetsimulations. Geophys Res Lett 2013;40:4109–4114.

43. Frierson DMW, Held IM, Zurita-Gotor P. A gray-radiationaquaplanet moist GCM. Part I: static stability and eddy scale. JAtmos Sci 2006;63:2548–2566.

44. Kang SM, Held IM, Frierson DMW, Zhao M. The response of theITCZ to extratropical thermal forcing: Idealized slab-ocean experi-ments with a GCM. J Climate 2008;21:3521–3532.

45. Taylor KE, Stouffer RJ, Meehl GA. An overview of CMIP5 and theexperiment design. Bull Amer Meteor Soc 2012;93(4):485–498.

46. Blackburn M, Williamson DL, Nakajima K, Ohfuchi W, TakahashiYO, Hayashi YY, Nakamura H, Ishiwatari M, McGregor JL, BorthH, et al. The aqua-planet experiment (APE): control SST simula-tion. J Meteorol Soc Japan 2013;91:17–56.

47. Walsh KJE, Camargo SJ, Vecchi GA, Daloz AS, Elsner J, EmanuelK, Horn M, Lim YK, Roberts M, Patricola C, et al. Hurricanes andclimate: the US CLIVAR working group on hurricanes. Bull AmerMeteor Soc 2015;96:997–1017.

48. Li F, Collins WD, Wehner MF, Leung LR. Hurricanes in anaquaplanet world: implications of the impacts of external forcingand model horizontal resolution. J Adv Model Earth Syst2013;5(2):134–145.

49. Zhou W, Held IM, Garner ST. Tropical cyclones in rotatingradiative–convective equilibrium with coupled SST. J Atmos Sci2017;74:879–892.

50. Bell MM, Montgomery MT, Emanuel KA. Air–sea enthalpy andmomentum exchange at major hurricane wind speeds observedduring CBLAST. J Atmos Sci 2012;69:3197–3222.

51. Emanuel K, DesAutels C, Holloway C, Korty R. Environmentalcontrol of tropical cyclone intensity. J Atmos Sci 2004;61:843–858.

52. Mei W, Xie S-P, Primeau F, McWilliams JC, Pasquero C.Northwestern pacific typhoon intensity controlled by changes inocean temperatures. Sci Adv 2015;1:e1500014.

53. Held IM, Zhao M. Horizontally homogeneous rotating radiative-convective equilibria at GCM resolution. J Atmos Sci 2008;65:2003–2013.

54. ZhouW, Held IM, Garner ST. Parameter study of tropical cyclonesin rotating radiative–convective equilibrium with column physicsand resolution of a 25-km GCM. J Atmos Sci 2014;71:1058–1069.

55. Khairoutdinov M, Emanuel K. Rotating radiative-convective equi-librium simulated by a cloud-resolving model. J Adv Model EarthSyst 2013;5:816–825.

56. Reed KA, Chavas DR. Uniformly rotating global radiative-convective equilibrium in the Community AtmosphereModel, ver-sion 5. J Adv Model Earth Syst 2015;7:1938–1955.

57. Chan JCL. The physics of tropical cyclonemotion. Annu Rev FluidMech 2005;37:99–128.

58. Held IM, Hou AY. Nonlinear axially symmetric circulations in anearly inviscid atmosphere. J Atmos Sci 1980;37:515–533.

59. Kirtman BP, Schneider EK. A spontaneously generated tropicalatmospheric general circulation. J Atmos Sci 2000;57:2080–2093.

60. Barsugli J, Shin SI, Sardeshmukh PD. Tropical climate regimes andglobal climate sensitivity in a simple setting. J Atmos Sci 2005;62:1226–1240.

61. Horinouchi T. Moist Hadley circulation: Possible role of wave-convection coupling in aquaplanet experiments. J Atmos Sci2012;69:891–907.

62. Pritchard MS, Yang D. Response of the superparameterizedMadden–Julian oscillation to extreme climate and basic-state vari-ation challenges a moisture mode view. J Climate 2016;29:4995–5008.

63. Walsh K. Climate theory and tropical cyclone risk assessment;2019.

64.• Chavas DR, Reed KA. 2019. Dynamical aquaplanet experimentswith uniform thermal forcing: implications for tropical cyclone

genesis and size. J. Atmos. Sci. https://doi.org/10.1175/JAS-D-19-0001.1. This article presents and compares theories for TCgenesis and size in spherical geometry, uniform thermalforcing simulations.

65.• Chavas DR, Reed KA, Knaff JA. Physical understanding of thetropical cyclone wind-pressure relationship. Nat Commun 2017;8:1360. This article presents a theory for the wind-pressure rela-tionship and assesses it in observations, comprehensive GCMsimulations, and uniform thermal forcing aquaplanetsimulations.

66. Corsaro CM. 2017. The β-effect in tropical cyclones: impact onintensity and sensitivity to temperature. Ph.D. thesis, ImperialCollege London, London UK.

67. Kossin JP. A global slowdown of tropical-cyclone translationspeed. Nature 2018;558:104–107.

68. Korty RL, Emanuel KA, Huber M, Zamora RA. Tropical cyclonesdownscaled from simulations with very high carbon dioxide levels.J Climate 2017;30:649–667.

69. Kossin JP, Emanuel KA, Vecchi GA. The polewardmigration of thelocation of tropical cyclone maximum intensity. Nature 2014;509:349–352.

70.• Fedorov AV, Muir L, Boos WR, Studholme J. 2018. Tropical cy-clogenesis in warm climates simulated by a cloud-system resolvingmodel. Clim. Dyn. pp. 1–21. This article investigates the effectsof meridional temperature gradients, approaching the weaktemperature gradient limit, on TC genesis in CRM simulations.

71. Bordoni S, Schneider T. Monsoons as eddy-mediated regime tran-sitions of the tropical overturning circulation. Nat Geosci 2008;1:515–519.

72. Donohoe A, Frierson DMW, Battisti DS. The effect of ocean mixedlayer depth on climate in slab ocean aquaplanet experiments. ClimDyn 2014;43:1041–1055.

73. Merlis TM. Does humidity’s seasonal cycle affect the annual-meantropical precipitation response to extratropical forcing. J Climate2016;29:1451–1460.

74. Byrne MP, Pendergrass AG, Rapp AD, Wodzicki KR. Response ofthe intertropical convergence zone to climate change: location,width, and strength. Current Climate Change Reports 2018;4:355–370.

75.• Seo J, Kang S, Merlis TM. A model intercomparison of the tropicalprecipitation response to a CO2 doubling in aquaplanet simulations.Geophys Res Lett 2017; 44: 993–1000. This article has an inter-comparison of ITCZ shifts in response to increased CO2 andshows that GCMs robustly simulate poleward shifts, with themagnitude sensitive to model parameterizations.

76. Bischoff T, Schneider T. Energetic constraints on the position of theintertropical convergence zone. J Climate 2014;27:4937–4951.

77. Emanuel K, Sobel A. Response of tropical sea surface temperature,precipitation, and tropical cyclone-related variables to changes inglobal and local forcing. J Adv Model Earth Syst 2013;5:447–458.

78. Sobel A, Camargo SJ, Hall TM, Lee CY, Tippett MK, Wing AA.Human influence on tropical cyclone intensity. Science 2016;353:242–246.

79. O’Gorman PA, Allan RP, Byrne MP, Previdi M. Energetic con-straints on precipitation under climate change. Surv Geophys2012;33:1–24.

80. Sobel A, Camargo SJ, Previdi M. 2019. Aerosol vs. greenhouse gaseffects on tropical cyclone potential intensity and the hydrologiccycle. J Climate p. in press.

81. Kim D, Moon Y, Camargo SJ, Wing AA, Sobel A, Murakami H,Vecchi GA, Zhao M, Page E. Process-oriented diagnosis of tropicalcyclones in high-resolution GCMs. J Climate 2018;31:1685–1702.

82. Camargo SJ, Emanuel KA, Sobel A. Use of a genesis potentialindex to diagnose ENSO effects on tropical cyclone genesis. JClimate 2007;20:4819–4834.

194 Curr Clim Change Rep (2019) 5:185–195

83. Vimont DJ, Kossin JP. The Atlantic meridional mode and hurricaneactivity. Geophys Res Lett 2007;34: L07709.

84.• Frisius T, Abdullah SMA. Nonlocality of tropical cyclone activityin idealized climate simulations. J Adv Model Earth Syst 2017;9:3099–3115. This article is the first TC-permitting GCM studywith idealized zonal asymmetries published.

85. Ballinger AP. 2015. Tropical cyclone activity in an aquaplanet gen-eral circulation model. Ph.D. thesis, Princeton University, PrincetonNJ.

86. Defforge C. 2016. Evaluating the influence of sea surface temper-ature on tropical cyclone genesis: observations and simulations.Master’s thesis, McGill University, Montreal, Canada.

87. Zarzycki CM, Levy MN, Jablonowski C, Overfelt JR, Taylor MA,Ullrich PA. Aquaplanet experiments using CAM’s variable-resolution dynamical core. J Climate 2014;27(14):5481–5503.

88. Harris LM, Lin SJ, Tu C. High-resolution climate simulations usingGFDL HiRAM with a stretched global grid. J Climate 2016;29:4293–4314.

89. Boos WR, Fedorov A, Muir L. Convective self-aggregation andtropical cyclogenesis under the hypohydrostatic rescaling. JAtmos Sci 2016;73:525–544.

90.• Wing AA, Reed KA, Satoh M, Stevens B, Bony S, Ohno T.Radiative-convective equilibrium model intercomparison project.Geosci Model Dev 2018;11:793–813. This article describes aprotocol for a non-rotating RCE intercomparison, includingGCMs and CRMs. Extending the protocol to rotating modelconfigurations is a promising approach for TC research.

91. Bretherton CS, Blossey PN, Khairoutdinov M. An energy-balanceanalysis of deep convective self-aggregation above uniform SST. JAtmos Sci 2005;62:4273–4292.

92. Muller CJ, Held IM. Detailed investigation of the self-aggregationof convection in cloud-resolving simulations. J Atmos Sci 2012;69:2551–2565.

93. Wing AA, Emanuel KA. Physical mechanisms controlling self-aggregation of convection in idealized numerical modeling simula-tions. J Adv Model Earth Syst 2014;6:59–74.

94. Bony S, Stevens B, Coppin D, Becker T, Reed KA, Voigt A,Medeiros B. Thermodynamic control of anvil cloud amount. ProcNat Acad Sci 2016;113:8927–8932.

95. Arnold NP, Randall DA. Global-scale convective aggregation: im-plications for the Madden-Julian Oscillation. J Adv Model EarthSyst 2015;7:1499–1518.

96. Muller CJ, Romps DM. Acceleration of tropical cyclogenesis byself-aggregation feedbacks. Proc Nat Acad Sci 2018;115:2930–2935.

Publisher’s Note Springer Nature remains neutral with regard to juris-dictional claims in published maps and institutional affiliations.

Curr Clim Change Rep (2019) 5:185–195 195